Solve: 16x² − 81 = 0.
x = 4, 9, x = - 4, - 9, x = 9 over 4, x = - 9/4, x = 81/16, x = - 81/16

Solution:

Given equation is 16x² − 81 = 0.

Step 1: Rewrite the equation in the form of a² - b² .

⇒ (4x)² - (9)² = 0

Step 2: By using the algebraic identity a² - b² = (a - b) (a + b)

⇒ (4x)² - (9)² = (4x - 9) (4x + 9)

Step 3: Put the solutions equal to 0.

Solving for x, we get

⇒ 4x - 9 = 0 or 4x = 9

⇒ 4x + 9 = 0 or 4x = -9

Therefore, x = ± 9/4.

Solve: 16x² − 81 = 0.
x = 4, 9, x = - 4, - 9, x = 9 over 4, x = - 9/4, x = 81/16, x = - 81/16

Summary:

The value of x which satisfies the equation 16x² − 81 = 0 is x = -9/4, 9/4.